Essentially, a mirror instance of SQL Server has the same dependencies as a non clustered instance (ignoring the mirrorred partner part of the equation)

Dependencies for a non clustered instance of SQL Server are pretty much taken care of by the OS.

• a valid computername
• a valid IP address
• disk(s) where the sql server binaries and data files are stored

At the service level in Windows the SQL Server agent depends upon the SQL Server service.

Now start throwing in AlwaysOn groups or AO groups and FCIs then you have a real headache for dependencies 😉